We study the problem of demonstration selection, which involves selecting a subset of examples for pre-pending to a query to a language model. This problem is closely related to in-context learning and model inference. Since the inference cost of a transformer model scales quadratically with sequence length, the selection problem becomes especially challenging in a long-context scenario. In this paper, we tackle this problem by building on state space models (SSMs), which has linear inference time given the input embeddings. Our approach works in two stages. First, we learn a small set of SSMs through a distillation procedure — given a (trained) transformer model, we partition all the layers into consecutive (layer) groups — for each group, we learn one SSM to mimic the input-output behavior, thereby capturing structural similarity in adjacent layers. Second, we map the SSM outputs to a small set of tokens, and apply them for downstream demonstration selection. We run extensive experiments in both synthetic and real-world datasets to validate this approach. We show that the SSMs trained from distillation incur a relative approximation error of less than 0.7%. As for downstream demonstration selection, we find that on several text classification and reasoning tasks, our approach reduces FLOPs by 14.2× and improves accuracy by 6.48% relative to baseline selection methods.

Two-sided digital platforms are inherently dynamic: user preferences shift, item popularity evolves, and reviews both reflect and drive these changes. Yet most sequential recommendation systems treat reviews as passive signals for updating user states, leaving two aspects underexplored. First, review generation is nonrandom, depending on evolving latent states of both users and items. Second, reviews can reshape item states, induce spillover across related items, and influence future user decisions. To address these gaps, we propose a two-sided state-space model (TS-SSM) for event-conditioned sequential recommendation. TS-SSM consists of three components: (1) a modality-missing-not-at-random fusion module that encodes review content and informative observation patterns; (2) user-state evolution with temporal variation and local graph message passing that uses related item states to refine user preferences; and (3) item-state evolution with asymmetric carryover of positive and negative review feedback. In experiments across six Amazon categories, TS-SSM increases Recall@20 over BSARec by 14.8%-18.8% and exceeds HM4SR by 11.7% on average. On Goodreads Fantasy, Recall@20 improves HM4SR from .5191 to .5847. Ablations highlight distinct contributions of observation patterns, local propagation, and item dynamics.

Multimodal clinical records contain structured measurements and clinical notes recorded over time, offering rich temporal information about the evolution of patient health. Yet these observations are sparse, and whether they are recorded depends on the patient’s latent condition. Observation patterns also differ across modalities, as structured measurements and clinical notes arise under distinct recording processes. While prior work has developed methods that accommodate missingness in clinical time series, how to extract and use the information carried by the observation process itself remains underexplored. We therefore propose a patient representation learning framework for multimodal clinical time series that explicitly leverages informative missingness. The framework combines (1) a multimodal encoder that captures signals from structured and textual data together with their observation patterns, (2) a Bayesian filtering module that updates a latent patient state over time from observed multimodal signals, and (3) downstream modules for offline treatment policy learning and patient outcome prediction based on the learned patient state. We evaluate the framework on ICU sepsis cohorts from MIMIC-III, MIMIC-IV, and eICU. It improves both offline treatment policy learning and adverse outcome prediction, achieving FQE 0.679 versus 0.528 for clinician behavior and AUROC 0.886 for post-72-hour mortality prediction on MIMIC-III.

Clinical notes contain rich patient information, such as diagnoses or medications, making them valuable for patient representation learning. Recent advances in large language models have further improved the ability to extract meaningful representations from clinical texts. However, clinical notes are often missing. For example, in our analysis of the MIMIC-IV dataset, 24.5% of patients have no available discharge summaries. In such cases, representations can be learned from other modalities such as structured data, chest X-rays, or radiology reports. Yet the availability of these modalities is influenced by clinical decision-making and varies across patients, resulting in modality missing-not-at-random (MMNAR) patterns. We propose a causal representation learning framework that leverages observed data and informative missingness in multimodal clinical records. It consists of: (1) an MMNAR-aware modality fusion component that integrates structured data, imaging, and text while conditioning on missingness patterns to capture patient health and clinician-driven assignment; (2) a modality reconstruction component with contrastive learning to ensure semantic sufficiency in representation learning; and (3) a multitask outcome prediction model with a rectifier that corrects for residual bias from specific modality observation patterns. Comprehensive evaluations across MIMIC-IV and eICU show consistent gains over the strongest baselines, achieving up to 13.8% improvement for hospital readmission and 13.1% for ICU admission (AUC, relative to best baseline).